Transforming Data
For a normally distributed data set, the mean is 20 and the standard deviation is 3.
I add 5 to all data points.
What is the new shape, mean and standard deviation?
Shape: still normal
Mean: 20+5=25
Standard deviation: still 3
A normal distribution has a mean = 230 and a standard deviation = 15. Find the following:
P(x < 210)
What is 0.0918
300 people took a test and I am the 4th best score. What is my percentile?
What is 99th percentile
Mean: 300
SD: 20
My Score: 280
What is the z-score?
What is -1
What percent of data is within 2 standard deviations in a Normal Distribution?
What is 95%
In a left-skewed data set, the median is 14 and the IQR is 4. I multiply each data point by 2. What are the new shape, median, and IQR?
Shape: still left skewed
Median: 14*2=28
IQR: 4*2=8
A normal model has a mean = 135 and a standard deviation = 10.4. Find the following : P(x > 146)
What is 0.1446
Find the z score that corresponds to the first quartile
What is -0.67
Mean: 30
SD: 2
My Score: 35
What is the z-score?
z=2.5
In a normal distribution, the mean is 200 and 68% of data is between 188 and 212. What is the standard deviation?
What is 12
In a normally distributed data set, the following summary statistics are known:
Mean: 42, Median: 40, Mode: 40
IQR: 6, Range: 20, Standard Deviation: 2
You add 4 then divide by 2 each value. What are the new summary statistics and shape?
shape: still normal
Mean: 23 Median: 22 Mode: 22
IQR: 3, Range: 10, St Dev: 1
A normal model has a mean = 86 and a standard deviation = 5. Find the following: P(85 < x < 95)
What is 0.5434
A normal distribution has a mean = 290 and a standard deviation = 37. Find the x value that represents the the 25th percentile.
What is 265.2
If a normal distribution has a mean = 290 and a standard deviation = 37. Find the z-score of 300
z=0.27
In a normal distribution, the mean is 200 and the standard deviation is 20. What value is at the 84th percentile?
What is 220?
At Columbus State, the average number of credits a students take in a semester is 12 with a standard deviation of 3.
Each credit costs $190. What is the mean and standard deviation for credit costs per semester?
Mean: 12*190= $2280
St Dev: 3*190= $570
A normal model has a mean = 17.1 and a standard deviation = 4. What x value represents the 75th percentile?
What is 19.78
A normal distribution has a mean = 127 and a standard deviation = 23.5. Find the x value that would correspond to the top 30%.
What is 139.22
Test A: z= -1.4
Test B: z= -0.3
Compare the z-scores
The person did better on Test B because the z-score was higher.
In a normal distribution, the mean is 50 and 95% of data is between 30 and 70. What is the standard deviation?
What is 10
At a rides carnival, the mean number of rides visitors ride is 6 with a standard deviation of 2.
The carnival costs $5 to enter and $3 per ride. What are the mean and standard deviation of paying for the carnival (assuming no cost for food, etc).
Mean: 5+6*3=$23
St Dev.: 2*3=$6
A normal model has a mean = 11.4 and a standard deviation = 3. Find the x value that represents the 5th percentile.
What is 6.47
Test A: Mean: 40, SD: 5, my score: 47
Test B: Mean: 81, SD: 3, my score: 84
Which test did I do better relatively?
Test A: z=1.4
Test B: z=1
Since 1.4 is greater I did better on Test A
In a normal distribution with mean 80 and standard deviation 5, what percent of data is between 65 and 90?
65 is 3 SDs below, so 0.15% is left
90 is 2 SDs above, so 97.5% is left
97.5-0.15=97.35%
What is 97.35%